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TitleThe regularity of Tor and graded Betti numbers.
Author(s) David Eisenbud, Craig Huneke, Bernd Ulrich
TypeArticle in Journal
AbstractLet S = K[x1, . . . , xn], let A, B be finitely generated graded S-modules, and let m = (x1, . . . , xn) ⊂ S. We give bounds for the regularity of the local cohomology of Tork (A, B) in terms of the graded Betti numbers of A and B, under the assumption that dim Tor1 (A, B) ≤ 1. We apply the results to syzygies, Gröbner bases, products and powers of ideals, and to the relationship of the Rees and symmetric algebras. For example we show that any homogeneous linearly presented m-primary ideal has some power equal to a power of m; and if the first [(n - 1)/2] steps of the resolution of I are linear, then I2 is a power of m.
ISSN0002-9327; 1080-6377/e
URL http://muse.jhu.edu/login?auth=0&type=summary&url=/journals/american_journal_of_mathematics/v128/128.3eisenbud.pdf
LanguageEnglish
JournalAm. J. Math.
Volume128
Number3
Pages573--605
PublisherJohns Hopkins University Press, Baltimore, MD
Year2006
Edition0
Translation No
Refereed No
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